Sir Thomas Rich's School are celebrating progression to the next round of the Under-18s Daily Mail Cup after a 46-22 victory over Colston's.
The Longlevens school are scheduled to face RGS High Wycombe away next Wednesday in the fifth round.
Tommies scored six tries, with full-back Tom Miles scoring two and scrum-half and captain Ollie Young also getting a brace.
The other tries were scored by Callum Wyman and Josh Vallender.
Outside half Ross Preedy kicked two penalties and five conversions to score 16 points.
There was also a strong performance from Sam Underhill who carried the ball well from the backrow, and drove lineouts skilfully too.
Deputy head Chris Carter said: "We have never played RGS High Wycombe before so we are very much looking forward to the challenge."